Rinse the wild rice under cold water and drain it well.
In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onions and sauté for about 3-4 minutes until translucent.
Add the minced garlic, diced celery, and carrots. Sauté for an additional 5 minutes until the vegetables begin to soften.
Stir in the sliced mushrooms and cook for another 3 minutes.
Add the rinsed wild rice, vegetable broth, water, thyme, parsley, salt, and black pepper to the pot. Increase the heat to high and bring the mixture to a boil.
Once boiling, reduce the heat to low, cover the pot, and let it simmer for about 25-30 minutes until the wild rice is tender.
If you prefer a thicker soup, mix the flour with a small amount of broth to create a slurry. Stir it into the soup and allow it to simmer for an additional 5 minutes.
Remove the pot from heat and stir in the heavy cream. Adjust seasoning with salt and pepper as necessary.
Serve hot, garnishing with fresh herbs if desired.